Chapter 8. Application of Random Walks to Bayesian Classification and Business Decision Making

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C. H. C. Leung1, PhD, Y. X. Li2, PhD and L. J. Hao3
1
School of Science and Engineering and Guangdong
Provincial Key Laboratory of Future Networks of Intelligence, Chinese University of Hong Kong, Shenzhen, China
2Department of Computer Science, Hong Kong Baptist University, Hong Kong, China
3School of Data Science, Chinese University of Hong Kong, Shenzhen, China

Part of the book: Advances in Business and Management. Volume 20

Abstract

Many decision-making scenarios can be viewed as classification problems. Classification decisions are pervasive and occur in many business situations. In many applications, classification problems do not occur in individually but in groups where several classification problems need to be solved. Examples of these include student admissions at colleges, whether or not to extend job offers to applicants, the effectiveness of advertising channels, and determining if COVID patients should be hospitalized. With any form of classification, however, there are unavoidable inaccuracies arising in different forms, especially when multiple classification tasks need to be performed. Since typical classifiers are not free from errors, classification errors tend to accumulate, and having frequent misclassifications are often unacceptable. Moreover, in unsupervised learning situations, there are typically no pre-determined ground truth classes; in such a situation the ground truth class is determined by the view of the majority of classifiers. In this chapter, we examine the situation of multiple classifications within the Naïve Bayes framework, where the ground truth is determined by the decision of most classifiers, and where there are finite resources requiring decisions to be made within a limited budget. Here, we represent the classification tasks as a one-dimension random walk process and perform a probabilistic analysis of the situation. We find that by raising the budget, the probability of error in classification can be controlled, and the extent of the reduction can be quantified. These results can be beneficially deployed in a variety of business decision[1]making situations in measuring and enhancing the quality of decisions.

Keywords: binary classification, naïve Bayes classifier, multiple classification, random walk, unsupervised learning


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